Yes tap water is safe in Shkodër, I was born there, grew up drinking that water. I live in New York and I can tell you that the water there has a diff taste regardless if it's tap or from a bottle, but make sure to keep very cold in the fridge so you won't notice the difference. Have fun while you're there. About the tourists, they're all gone by the end of August.

I mostly drank bottled water in Albania this summer but if I don't remember horribly wrong, I did have tap water too while in Saranda (in the very south), and had no problems. (I probably asked the very helpful owner and other guests at Backpackers SR who said it's ok.)

That said, Shkodër is at the opposite end of the country, and I guess the water quality can depend on the exact locality and even the building (the house I stayed in was pretty new / in good shape).

I'd ask locals in each town, and you'll probably meet some foreigners too, eventually, who you can consult. If in doubt, better to err on the safe side, of course.

Edit: One friend said:

I usually drink tap water when in Albania, but because I'm most of the
time in the streets or at the beach, I have to get bottled water
along. Other than that it is safe to drink the tap water there in most
places... Durres is a bit suspicious since there are too many people
during the summer and the water can get more polluted, but this is my
personal opinion!

(She's a medical student from Kosovo who's been to Albania many times.)

I think it's understandable why guidebooks and officials should "play it safe" by advising you to stick to bottled water, even if in reality the risks were not that big these days. Albania remains somewhat "exotic" and not so well-known destination, for a European country. Disclaimer: in every case, do it at your own responsibility. :-)

I just spent a week in Albania and did drink the tab water everywhere (actually I've only been to Tirana, Berat, Saranda and Korca). In Tirane the people at the hostel did drink the water themselves but didn't recommend it to me, just to be on the safe side.